Answer to Question #350297 in Physics for Geral

Question

If the gravitational field strength at the top of Mount Everest is 9.772 N/kg, approximately how tall (in

feet) is the mountain?

Answer 1

$g(h)=G\frac{M}{(R+h)^2}=G\frac{M}{R^2}*\frac{R^2}{(R+h)^2}$

$g(h)=g(0)\frac{R^2}{(R+h)^2}$

$9.772=9.807*\left(\frac{6378}{6378+h}\right)^2$

$\frac{6378}{6378+h}=0.998$

$h=11.41\:\rm km=37 434\: ft$